MCQs in Plane Geometry Part I

This is the Multiple Choice Questions Part 1 of the Series in Plane Geometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

Start Practice Exam Test Questions Part I of the Series

Find the angle in mills subtended by a line 10 yards long at a distance of 5000 yards.

A. 1

B. 2

C. 2.5

D. 4

Problem 2: ECE Board April 1999

Assuming that the earth is sphere whose radius is 6400 km. Find the distance along a 3 degree arc at the equator of the earth’s surface.

A. 335.10 km

B. 533.10 km

C. 353.10 km

D. 353.01 km

Problem 3: EE Board April 1992

The angle subtended by an arc is 24o. If the radius of the circle is 45 cm, find the length of arc

A. 16.85 cm

B. 17.85 cm

C. 18.85 cm

D. 19.85 cm

Problem 4: ME Board April 1990

A rat feel on a bucket of a water wheel with diameter of 600 cm which travelled an angle of 190obefore it dropped from the bucket. Calculate for the linear cm that the rat was carried by the bucket before it fell.

A. 950

B. 965

C. 985

D. 995

Problem 5: ECE Board November 1992

Given the circle whose diameter AB equals 2 m. If two points C and D lie on the circle and angles ABC and BAD are 18o and 36o, respectively, find the length of the major arc CD.

A. 1.26 m

B. 1.36 m

C. 1.63 m

D. 1.45 m

Problem 6:

A certain angle has as supplement 5 times its complement. What is the angle?

A. 67.5o

B. 58.5o

C. 30o

D. 27o

Problem 7: ECE Board November 1998

Each angle of a regular dodecagon is equal to

A. 135o

B. 150o

C. 125o

D. 105o

Problem 8: CE Board May 1997

How many sides has a polygon if the sum of the interior angles is 1080o?

A. 5

B. 6

C. 7

D. 8

Problem 9: ECE Board March 1996

The sum of the interior angles of a polygon is 540o. Find the number of sides.

A. 3

B. 4

C. 5

D. 6

Problem 10: ECE Board April 1991

Find the sum of the interior angles of the vertices of a five pointed star inscribed in a circle.

A. 150o

B. 160o

C. 170o

D. 180o

Problem 11: ME Board April 1999

How many sides are in a polygon if each interior angle is 165 degrees.

A. 12

B. 24

C. 20

D. 48

Problem 12:

How many diagonals are there in a polygon of 20 sides?

A. 200

B. 170

C. 100

D. 158

Problem 13: ME Board April 1999

Find each interior angle of a hexagon.

A. 90o

B. 120o

C. 150o

D. 180o

Problem 14: EE Board April 1994

Given a triangle, C = 100o, A = 15 m, B = 20 m. Find C.

A. 26 m

B. 27 m

C. 28 m

D. 29 m

Problem 15: CE Board November 1994

In triangle ABC, angle A = 45o and C = 70o. The side opposite angle C is 40 m long. What is the length of the side opposite angle A?

A. 26.1 m

B. 27.1 m

C. 29.1 m

D. 30.1 m

Problem 16: CE Board May 1995

In triangle ABC, angle C = 70o, A= 45o, AB = 40 m. What is the length of the median drawn from vertex A to side BC?

A. 36.3 m

B. 36.6 m

C. 36.9 m

D. 37.2 m

Problem 17: EE Board April 1991

From a point outside of an equilateral triangle, the distances to the vertices are 10 m, 18 m and 10 m, respectively. What is the length of one side of a triangle?

A. 17.75 m

B. 18.50 m

C. 19.95 m

D. 20.50 m

Problem 18: EE Board April 1991

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the inscribed circle.

A. 2.25 cm

B. 2.35 cm

C. 2.45 cm

D. 2.55 cm

Problem 19: CE Board May 1996

What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm.?

A. 12.73 m

B. 13.52 m

C. 14.18 m

D. 15.55 m

Problem 20: EE Board April 1991

The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the circumscribing circle.

A. 7.14 cm

B. 7.34 cm

C. 7.54 cm

D. 7.74 cm

Problem 21: CE Board May 1996

Two sides of a triangle are 50 m and 60 m long. The angle included between these sides is 30o. What is the interior angle opposite the longest side?

A. 93.74o

B. 92.74o

C. 90.74o

D. 86.38o

Problem 22: ECE Board March 1996

A circle with radius 6 cm has half its area removed by cutting off a border of uniform width. Find the width of the border.

A. 1.76 cm

B. 1.35 cm

C. 1.98 cm

D. 2.03 cm

Problem 23: ME Board April 1996

The area of a circle is 89.42 sq. inches. What is its circumference?

A. 32.25 in.

B. 33.52 in.

C. 35.33 in.

D. 35.55 in.

Problem 24: ECE Board April 1991

A square section ABCD has one of its sides equal to x. Point E is inside the square forming an equilateral triangle BEC having one side equal in length to the side of the square. Find the angle AED.

A. 130o

B. 140o

C. 150o

D. 160o

Problem 25: CE Board November 1995

The area of a circle circumscribing about an equilateral triangle is 254.47 sq. m. What is the area of the triangle in sq. m?

A. 100.25

B. 102.25

C. 104.25

D. 105.25

Problem 26: CE Board May 1995

What is the area in sq. cm of the circle circumscribed about an equilateral triangle with a side 10 cm long?

A. 104.7

B. 105.7

C. 106.7

D. 107.7

Problem 27: CE Board November 1992

The area of a triangle inscribed in a circle is 39.19 cm2 and the radius of the circumscribed circle is 7.14 cm. If the two sides of the inscribed triangle are 8 cm and 10 cm, respectively, find the third side.

A. 11 cm

B. 12 cm

C. 13 cm

D. 14 cm

Problem 28: CE Board November 1994

The area of a triangle is 8346 sq. m and two of its interior angles are 37o25’ and 56o17’. What is the length of the longest side?

A. 171.5 m

B. 181.5 m

C. 191.5 m

D. 200.5 m

Problem 29: ECE Board April 1998

The angle of a sector is 30o and the radius is 15 cm. What is the area of the sector in cm2?

A. 59.8

B. 89.5

C. 58.9

D. 85.9

Problem 30: EE Board April 1992

Two perpendicular chords both 5 cm from the center of a circle divide the circle into four parts. If the radius of the circle is 13 cm, find the area of the smallest part.

A. 30 cm2

B. 31 cm2

C. 32 cm2

D. 33 cm2

Problem 31: ECE Board April 1998

The distance between the centers of the three circles which are mutually tangent to each other externally are 10, 12, and 14 units. The area of the largest circle is?

A. 72 π

B. 23 π

C. 64 π

D. 16 π

Problem 32: ECE Board November 1993

The arc of a sector is 9 unites and its radius is 3 units. What is the area of the sector in square units?

A. 12.5

B. 13.5

C. 14.5

D. 15.5

Problem 33: CE Board May 1998

A circle having an area of 452 sq. m is cut into two segments by a chord which is 6 m from the center of the circle. Compute the area of the bigger segment.

A. 354. 89 sq. m

B. 363. 68 sq. m

C. 378. 42 sq. m

D. 383. 64 sq. m

Problem 34: ECE Board April 1992

A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a radius of 9 m and each circle passes through the center of the other. Find the area of the swimming pool.

A. 380 m2

B. 390 m2

C. 400 m2

D. 410 m2

Problem 35: ME Board April 1991

Find the difference of the area of the square inscribe in a semi-circle having a radius of 15 ,. The base of the square lies on the diameter of the semi-circle.

A. 171.5 cm2

B. 172.5 cm2

C. 173.5 cm2

D. 174.5 cm2

Problem 36: ECE Board November 1995

A rectangle ABCD which measures 18 cm. by 24 cm. is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.

A. 20.5 cm2

B. 21.5 cm2

C. 22.5 cm2

D. 23.5 cm2

Problem 37: ECE Board April 1998

A trapezoid has an area of 36 m2 and an altitude of 2 m. Its two bases have the ration of 4:5. What are the lengths of the bases?

A. 12, 15

B. 7, 11

C. 8, 10

D. 16, 20

Problem 38: EE Board March 1998

A rhombus has diagonals of 32 and 20 inches. Determine its area.

A. 360 in2

B. 280 in2

C. 320 in2

D. 400 in2

Problem 39: ECE Board April 1998

If the sides of a parallelogram and an included angle are 6, 10 and 100o, respectively, find the length of the shorter diagonal.

A. 10.63

B. 10.37

C. 10.73

D. 10.23

Problem 40: CE Board November 1996

Find the area of a quadrilateral having sides AB = 10 cm, BC = 5 cm, CD = 14.14 cm and DA = 15 cm, if the sum of the opposite angles is equal to 225o.

Find the area of a quadrilateral have sides 12 m, 20 m, 8 m and 16.97 m. If the sum of the opposite angles is equal to 225o, find the area of the quadrilateral.

A. 100 m2

B. 124 m2

C. 168 m2

D. 158 m2

Problem 43: ME Board October 1996, ME Board April 1997

The area of a regular hexagon inscribed in a circle of radius 1 is?

A. 1.316

B. 2.945

C. 2.598

D. 3.816

Problem 44: EE Board April 1990

Find the area (in cm2) of a regular octagon inscribed in a circle of radius 10 cm?

A. 283

B. 289

C. 298

D. 238

Problem 45: GE Board February 1992

A regular hexagon is inscribed in a circle whose diameter is 20 m. Find the area of the 6 segments of the circle formed by the sides of the hexagon.

A. 36. 45 sq. m

B. 63. 54 sq. m

C. 45. 63 sq. m

D. 54. 36 sq. m

Problem 46: EE Board April 1993

Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.

A. 1075 m2

B. 1085 m2

C. 1080 m2

D. 1095 m2

Problem 47: ME Board October 1996

The area of a circle is 89.42 sq. inches. What is the length of the side of a regular hexagon inscribed in a circle?

A. 5.533 in.

B. 5.335 in.

C. 6.335 in.

D. 7.335 in.

Problem 48: EE Board April 1990

In a circle of diameter of 10 m, a regular five-pointed star touching its circumference is inscribed. What is the area of that part not covered by the star?

A. 40. 5 sq. m

B. 45. 5 sq. m

C. 50. 5 sq. m

D. 55. 5 sq. m

Problem 49: EE Board March 1998

A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the large pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon.

A. 430.70 cm3

B. 573.26 cm3

C. 473.77 cm3

D. 516.14 cm3

Problem 50: EE Board March 1999

Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.